The Brazilian made the move from Wolfsburg on Friday, having spent a season on loan at the Vicente Calderon in 2011.
He had been with the Bundesliga side since 2010 and Diego admitted that Simeone's influence was one of the main forces behind his decision to move.
"My relationship with Simeone was always spectacular," he said at his unveiling on Monday. "He's the best coach I worked with in my life. He helps a lot as a player and person.
"That confidence he has in me has made a difference in the decisions I have made."
Diego enjoyed a goalscoring return to the club as he registered the final effort in Atletico's 4-0 win over Real Sociedad on Sunday.
It moved Simeone's men top of La Liga but Diego has not been surprised by Atletico's form, having been impressed with what he saw during his loan spell.
"When I came here it was a very well organised team, on the right path," he added.
"Today it is an even stronger team and I'm here to go the full way with them and help the team keep winning.
"It will be a very difficult game playing Real Madrid (in the Copa Del Rey on Wednesday), but we are prepared to play a great game.
"We will prepare to win the game, but with confidence."
